The terahertz (THz) region of the electromagnetic spectrum is one of the least developed spectral regions due to the limited number of sources, detectors, and devices available. However, many emerging applications have been identified. This work explores plasmon modes resonantly excited by THz radiation in double quantum well (DQW) field effect transistors with views of developing a tunable THz detector. The plasmon modes are probed as a function of gate voltage, temperature, frequency, in-plane magnetic field and polarization of the THz radiation. The samples used were DQWs patterned into mesas with a metal grating gate and ohmic contacts. We observe sharply resonant, voltage tuned THz photoconductivity that we can semi-quantitatively model by two dimensional standing plasma oscillations under the grating gate. The resonant frequency is directly related to the electron densities and the period of the grating. These results suggest that one could develop a fast, tunable THz detector based on two dimensional plasma oscillations of coupled DQWs. This work would be of interest for students, scientists and engineers interested in plasmon modes, THz technology and detection.